Proving max (a,b) = \frac{a+b + \left|a+b\right|}{2}

[The_Iceflash]

Homework Statement

Prove max (a,b) = $$\frac{a+b + \left|a+b\right|}{2}$$

Make 3 cases:

Case 1: Assume a > b. Show both sides come out with the same number.
Case 2: Assume a < b. Show both sides come out with the same number.
Case 3: Assume a = b. Show both sides come out with the same number.

Homework Equations

N/A

The Attempt at a Solution

To be honest I'm not sure how to set up both sides to begin with before I even start to break it down to address each case. Once I see how to do that I should be able to be able to prove this.

 

[statdad]

First make sure you have the correct statement: if you check your expression for a = 5, b = 10, you get

$$\frac{5+10 + |5+10|}{2} = \frac{15 + 15} 2 = 15$$

which is not the maximum of the numbers 5 and 10. Perhaps it should be

$$\max(a,b) = \frac{(a+b) + |a-b|}{2}$$

Consider your final case: if $$a = b$$, what can you say about which one is the maximum? Then, what can you say about how the right-side simplifies if the two inputs are equal?